ON THE GENEEALISED PEOBABLE ERKOE IN 
MULTIPLE NOEMAL COEEELATION. 
By. KARL PEARSON, F.R.S., and ALICE LEE, D.Sc. 
The normal correlation surface in the case of n variables is known to be : 
where 
R 
1 ) '''12 ) ''13 J • • • 'Yft 
1 
and Rpij is the minor corresponding to the constituent r^,. S denotes a sum for 
all values of p from 1 to n, and S' a sum for every pair of unlike p, q's. Xp is the 
^th variate measured from its mean, ap its standard deviation and Tpq the correla- 
tion coefficient of the jjth and qXh. variates. 
Let 
= ^ {'S^ {Rpp-'Vp-/<Tf) + 28' {Rp,jX.i,xJapa,j)]. 
Then %" = a constant, is the equation to an ellipsoid in ?i.-fold space. If transferred 
to its principal axes, it will take the form 
n 
X^ = S{Xp^/tp^). 
Further: zdw^^dxi ... dxn will equal 
N 1 
^ — e - dX, dX.... dXn , 
(27r)i«2.2....2„ 
representing the frequency due to n independent variates. 
